Hilbert's Inequality

We prove Hilbert's integral inequality where one considers the kernel 1/(x+y) over the first quadrant. After several changes of variables, we are able to apply Cauchy-Schwarz to prove the boundedness of this operator. This result can be discretized to prove that the Hilbert matrix is bounded on l^2.

#mikethemathematician, #mikedabkowski, #profdabkowski

[Andrew_J]

Are you making a measure theory playlist?